What you are saying is, in theory, the basis for any sensible rescue attempt. But the victim was in 20 feet of water ... an adequately trained diver should have been able, in my opinion, to free dive down 20 feet and recover an inert diver, and 400 psi is more than enough for a quick bounce to 20 feet. Granted that viability could effect this.
That opinion, would in all but the very smallest handfull of cases, most likely result in another family paying for a funeral. Do it the right way or just don't do it at all. Its very simple stuff. The time for heroics is in the set up and execution of your dives. Once its a rescue or recovery, only a fool adds risk to an already out of hand situation.